Plurisubharmonic functions and nef classes on complex manifolds

TL;DR

This paper establishes the existence of specific plurisubharmonic functions with prescribed singularities on complex manifolds, advancing the understanding of nef classes and their properties in complex geometry.

Contribution

It proves the existence of such functions on complex 3-folds with nef classes and positive volume, and extends the result to rational classes on Moishezon n-folds, providing new tools in complex geometry.

Findings

Existence of plurisubharmonic functions with prescribed singularities on complex 3-folds.

Extension of results to rational classes on Moishezon n-folds.

Advancement in understanding nef classes and their associated functions.

Abstract

We prove the existence of plurisubharmonic functions with prescribed logarithmic singularities on complex 3-folds equipped with a nef class of positive volume. We prove the same result for rational classes on Moishezon n-folds.